| 李振亨,靳一东,白瑞蒲.一类特殊广义Kac-Moody代数虚根决定的反射与Weyl群间的关系(英)[J].数学研究及应用,1999,19(3):501~507 |
| 一类特殊广义Kac-Moody代数虚根决定的反射与Weyl群间的关系(英) |
| Relationship between Reflections Determined by Imaginary Roots and the Weyl Group for a Special GKM Algebra |
| 投稿时间：1996-07-22 |
| DOI：10.3770/j.issn:1000-341X.1999.03.006 |
| 中文关键词: |
| 英文关键词:generalized Kac-Moody algebra imaginary root system the Weyl group special imaginary root |
| 基金项目: |
|
| 摘要点击次数: 2559 |
| 全文下载次数: 1073 |
| 中文摘要: |
| 对有限型李代数g（A），相应于每个根α的反射rα均在g（A）的Weyl群W中．当g（A）为可对称化的不定型Kac－Moody代数时，若α为一虚根且（α，α）＜0，则亦可定义反射rα并有rα∈－W或rα是－W中元与一个图自同构之积（见[3]）．本文给出了一类秩为3的广义Kac－Moody代数的虚根系，然后讨论了一类特殊的广义Kac－Moody代数的虚根决定的反射与Weyl群之间的关系． |
| 英文摘要: |
| It's well known that a reflectin rα associated to every root α belongs to the Weyi group of a Lie algebra g(A) of finite type. When g(A) is a symmetrizable Kac-Moody algebra of indefinite type, one of can define a reflection rα for every imzginary root α satisfying (α, α) < 0. From [3] we know rα ∈-W or rα is an element of-W mutiplied by a diagram automorphism . How about the relationship between reflections associated to imaginary root and the Weyl group of a symmetrized Kac-Moody algebra (GKM algebra for short)? We shall discuss it for a special GKM algebra in present paper (see 3). In sections 1 and 2 we introduce some basic concepts and give the set of imaginary roots of a class of rank 3 GKM algebras. |
| 查看全文 查看/发表评论 下载PDF阅读器 |
